Analyses
Non preregistered analyses - alternative Bayesian metaanalytic models
Ian Hussey
19 November 2020
The original preregistrations for the studies contained both hypotheses and the specific analytic strategies that would be used to test them. However, these preregistrations did not include a meta-analytic strategy. Separately, a number of research questions/hypotheses were generated from exploration of the data from Experiments 1-6 that were not contained in the original preregistration, or where the specific analytic strategy to test them was poorly specified or more difficult to interpret. Separately, some methodological improvements were thought of after Experiments 1-6 was run (e.g., improved exclusion criteria to ensure participants stayed on the page where they watched/listened to the intervention in its entirety). We therefore elected to use the data from Experiments 1-6 to create this (non-preregistered) alternative analytic strategy that formalized our core research questions, hypotheses, analytic models, inference rules, and other researcher degrees of freedom. This analytic strategy (and code to implement it) will be preregistered for Experiment 7 which will provide strong confirmatory tests of these hypotheses.
Dependencies & functions
# dependencies
library(tidyverse)
library(knitr)
library(kableExtra)
library(brms)
library(parallel)
library(tidybayes)
library(bayestestR)
library(sjPlot)
library(psych)
library(rsample)
library(broom)
library(purrr)
library(IATscores)
library(lavaan)
library(semTools)
library(modelr)
options(knitr.kable.NA = "/")
# set seed for bootstrapping reproducibility
set.seed(42)
# create necessary folder
dir.create("models")Exclusions & standaridization
All dependent variables (self-reported evaluations and IAT D2 scores) were standardized (by 1 SD) after exclusions and prior to analysis condition (see Lorah, 2018: https://doi.org/10.1186/s40536-018-0061-2). This was done within each level of both IV (i.e., by Source Valence condition [positive vs. negative], and by Video Content [Genuine vs. Deepfaked]). As such, the beta estimates obtained from the Bayesian models (see research questions and data analysis plans below) therefore represent standardized beta values (\(\beta\) rather than \(B\)). More importantly, the nature of this standardization makes these estimates somewhat comparable to the frequentist standardized effect size metric Cohen’s \(d\), as both are a differences in (estimated) means as a proportion of SD although they should not be treated as equivalent. Effect size magnitude here can therefore be thought of along comparable scales as Cohen’s \(d\). As such, to aid interpretability, the point estimates of effect size will be reported as \(\delta\) (delta).
# full data
data_processed <- read.csv("../data/processed/4_data_participant_level_with_hand_scoring.csv") %>%
# set factor levels for t test comparisons
mutate(source_valence = fct_relevel(source_valence,
"negative",
"positive"),
experiment_condition = fct_relevel(experiment_condition,
"genuine",
"deepfaked"),
experiment = as.factor(experiment))
# apply exclusions
data_after_exclusions <- data_processed %>%
filter(exclude_subject == FALSE &
exclude_implausible_intervention_linger == FALSE) %>%
# standardize DVs by 1SD within each experiment and their conditions
group_by(experiment, experiment_condition, source_valence) %>%
mutate(mean_self_reported_evaluation = mean_self_reported_evaluation/sd(mean_self_reported_evaluation),
IAT_D2 = IAT_D2/sd(IAT_D2),
mean_intentions = mean_intentions/sd(mean_intentions)) %>%
ungroup()
# item level for iat
data_iat_item_level_after_exclusions <- read_csv("../data/processed/2.4_data_iat_item_level.csv") %>%
# exclude the same participants as above
semi_join(rename(data_after_exclusions, subject_original = subject), by = "subject_original") Distributions
ggplot(data_after_exclusions, aes(mean_self_reported_evaluation, color = experiment)) +
geom_density() +
facet_wrap( ~ experiment_condition + source_valence) +
ggtitle("Standardized scores")
ggplot(data_after_exclusions, aes(IAT_D2, color = experiment)) +
geom_density() +
facet_wrap( ~ experiment_condition + source_valence) +
ggtitle("Standardized scores")
ggplot(data_after_exclusions, aes(mean_intentions, color = experiment)) +
geom_density() +
facet_wrap( ~ experiment_condition + source_valence) +
ggtitle("Standardized scores")
Demographics
Pre exclussion
data_processed %>%
group_by(experiment) %>%
summarise(n = n(),
excluded_n = sum(exclude_subject > 0 | exclude_implausible_intervention_linger > 0),
excluded_percent = (excluded_n / n) *100) %>%
mutate_if(is.numeric, round, digits = 1) %>%
kable(align = "c") %>%
kable_styling()| experiment | n | excluded_n | excluded_percent |
|---|---|---|---|
| 1 | 165 | 24 | 14.5 |
| 2 | 167 | 36 | 21.6 |
| 3 | 428 | 91 | 21.3 |
| 4 | 429 | 106 | 24.7 |
| 5 | 276 | 66 | 23.9 |
| 6 | 265 | 61 | 23.0 |
Post exclusions
data_after_exclusions %>%
group_by(experiment) %>%
summarise(n = n(),
age_mean = mean(age, na.rm = TRUE),
age_sd = sd(age, na.rm = TRUE)) %>%
mutate_if(is.numeric, round, digits = 1) %>%
kable(align = "c") %>%
kable_styling()| experiment | n | age_mean | age_sd |
|---|---|---|---|
| 1 | 141 | 29.7 | 7.6 |
| 2 | 131 | 31.1 | 7.3 |
| 3 | 337 | 29.8 | 8.7 |
| 4 | 323 | 30.1 | 9.0 |
| 5 | 210 | 31.2 | 11.5 |
| 6 | 204 | 33.3 | 12.5 |
data_after_exclusions %>%
count(experiment, gender) %>%
spread(gender, n) %>%
kable(knitr.kable.NA = "/", align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| experiment | female | male | Non-binary | other | Prefer not to disclose |
|---|---|---|---|---|---|
| 1 | 67 | 73 | / | 1 | / |
| 2 | 76 | 55 | / | / | / |
| 3 | 184 | 149 | / | 4 | / |
| 4 | 189 | 132 | / | 2 | / |
| 5 | 119 | 88 | 2 | / | 1 |
| 6 | 120 | 82 | 2 | / | / |
Internal consistency
Self-reported evaluations
model_sr <- "scale =~ ratings_bad_good + ratings_dislike_like + ratings_negative_positive"
fit_cfa_sr <- data_after_exclusions %>%
cfa(model = model_sr, data = .)
results_reliability_sr <- fit_cfa_sr %>%
reliability() %>%
as.data.frame() %>%
rownames_to_column(var = "metric") %>%
select(metric, estimate = scale) %>%
filter(metric %in% c("alpha",
"omega2")) %>%
mutate(metric = recode(metric,
"alpha" = "alpha",
"omega2" = "omega_t"),
estimate = round(estimate, 3))
results_reliability_sr %>%
kable(knitr.kable.NA = "/", align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| metric | estimate |
|---|---|
| alpha | 0.987 |
| omega_t | 0.987 |
IAT
split half
results_iat_split_half_reliability <- data_iat_item_level_after_exclusions %>%
SplitHalf.D2(IATdata = .) %>%
mutate(algorithm = ifelse(algorithm == "p2112", "D2", algorithm),
splithalf = round(splithalf, 3))## [1] "2020-11-19 14:54:23: Applying parameter P4 = dist"
## [1] "2020-11-19 14:54:23: Applying parameters P1 and P2"
## [1] "2020-11-19 14:54:23: Applying parameter P3 = dscore"
## [1] "2020-11-19 14:54:23: Applying parameters P1 and P2"
## [1] "2020-11-19 14:54:24: Applying parameter P3 = dscore"
## [1] "2020-11-19 14:54:24: IAT scores have been computed"
## [1] "2020-11-19 14:54:24: Applying parameter P4 = dist"
## [1] "2020-11-19 14:54:24: Applying parameters P1 and P2"
## [1] "2020-11-19 14:54:24: Applying parameter P3 = dscore"
## [1] "2020-11-19 14:54:25: Applying parameters P1 and P2"
## [1] "2020-11-19 14:54:25: Applying parameter P3 = dscore"
## [1] "2020-11-19 14:54:25: IAT scores have been computed"results_iat_split_half_reliability %>%
kable(knitr.kable.NA = "/", align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| algorithm | splithalf |
|---|---|
| D2 | 0.839 |
Behavioral intentions
model_bi <- "scale =~ behavioral_intentions_share + behavioral_intentions_subscribe + behavioral_intentions_recommend"
fit_cfa_bi <- data_after_exclusions %>%
cfa(model = model_bi, data = .)
results_reliability_bi <- fit_cfa_bi %>%
reliability() %>%
as.data.frame() %>%
rownames_to_column(var = "metric") %>%
select(metric, estimate = scale) %>%
filter(metric %in% c("alpha",
"omega2")) %>%
mutate(metric = recode(metric,
"alpha" = "alpha",
"omega2" = "omega_t"),
estimate = round(estimate, 3))
results_reliability_bi %>%
kable(knitr.kable.NA = "/", align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| metric | estimate |
|---|---|
| alpha | 0.941 |
| omega_t | 0.941 |
Can you establish evaluations via genuine and Deepfaked online content?
- Analyses employ Bayesian multilevel models with experiment employed as a random (Group level) intercept, and source_valence, experiment_condition and their interaction as IVs. This could therefore be described as akin to a Bayesian multilevel ANOVA.
- DVs were standardize as noted above, and as such fitted model estimates represent standardized beta values (which due to the specifics of the standardization have comparable [but not exact] interpretation as Cohen’s d values).
- Bayesian p values are also reported: these are on a similar scale to frequentist p values, but technically are 1 minus the posterior probability that the effect is greater than 0, i.e., \(1 - P(\beta>0)\).
- Inspection of the posterior distributions allow us to infer that we employed weak priors placed on all parameters (normal distribution with M = 0 and SD = 10). Inspection of the chains indicated good convergence in all cases.
Sample sizes
data_after_exclusions %>%
select(source_valence,
experiment_condition) %>%
drop_na() %>%
count(experiment_condition,
source_valence) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| experiment_condition | source_valence | n |
|---|---|---|
| genuine | negative | 382 |
| genuine | positive | 425 |
| deepfaked | negative | 257 |
| deepfaked | positive | 282 |
Self-reported evaluations
Fit model
fit_selfreport <-
brm(formula = mean_self_reported_evaluation ~ source_valence * experiment_condition + (1 | experiment),
family = gaussian(),
data = data_after_exclusions,
file = "models/fit_selfreport",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: mean_self_reported_evaluation ~ source_valence * experiment_condition + (1 | experiment)
## Data: data_after_exclusions (Number of observations: 1346)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Group-Level Effects:
## ~experiment (Number of levels: 6)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.18 0.11 0.06 0.46 1.00 5768 9514
##
## Population-Level Effects:
## Estimate Est.Error
## Intercept -1.48 0.10
## source_valencepositive 2.70 0.07
## experiment_conditiondeepfaked 0.08 0.09
## source_valencepositive:experiment_conditiondeepfaked 0.01 0.12
## l-95% CI u-95% CI Rhat
## Intercept -1.68 -1.28 1.00
## source_valencepositive 2.56 2.85 1.00
## experiment_conditiondeepfaked -0.09 0.25 1.00
## source_valencepositive:experiment_conditiondeepfaked -0.22 0.24 1.00
## Bulk_ESS Tail_ESS
## Intercept 8855 10218
## source_valencepositive 16019 18209
## experiment_conditiondeepfaked 14109 17038
## source_valencepositive:experiment_conditiondeepfaked 13233 16420
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.03 0.02 1.00 1.07 1.00 22065 19280
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_selfreport) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
| b_experiment_conditiondeepfaked | uninformative |
| b_source_valencepositive.experiment_conditiondeepfaked | uninformative |
Interpret posteriors
# plot_model(fit_selfreport)
plot_model(fit_selfreport, type = "pred", terms = c("source_valence", "experiment_condition"))
# percent moderation
draws_sr <-
bind_cols(
select(spread_draws(fit_selfreport, b_source_valencepositive), b_source_valencepositive),
select(spread_draws(fit_selfreport, b_experiment_conditiondeepfaked), b_experiment_conditiondeepfaked),
select(spread_draws(fit_selfreport, `b_source_valencepositive:experiment_conditiondeepfaked`), `b_source_valencepositive:experiment_conditiondeepfaked`)
) %>%
rename(main_valence = b_source_valencepositive,
main_experiment_condition = b_experiment_conditiondeepfaked,
interaction = `b_source_valencepositive:experiment_conditiondeepfaked`) %>%
mutate(effect_genuine = main_valence,
effect_deepfaked = main_valence + main_experiment_condition + interaction,
#percent_moderation = (main_experiment_condition + interaction)/main_valence *100, # alt method, same result
percent_comparison = (effect_deepfaked/effect_genuine)*100)
# results
estimates_sr <-
map_estimate(draws_sr) %>%
full_join(bayestestR::hdi(draws_sr, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_sr, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_sr %>%
select(-percent_comparison) %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
# results table
estimates_sr %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| main_valence | 2.70 | 2.56 | 2.85 | 2.58 | 2.82 | 0.0000000 |
| main_experiment_condition | 0.08 | -0.09 | 0.25 | -0.07 | 0.22 | 0.1813214 |
| interaction | 0.01 | -0.22 | 0.23 | -0.18 | 0.20 | 0.4719643 |
| effect_genuine | 2.70 | 2.56 | 2.85 | 2.58 | 2.82 | 0.0000000 |
| effect_deepfaked | 2.78 | 2.63 | 2.95 | 2.66 | 2.93 | 0.0000000 |
| percent_comparison | 103.32 | 97.29 | 109.36 | 98.05 | 108.21 | / |
# hypothesis testing
H1a <- ifelse((estimates_sr %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H1b <- ifelse((estimates_sr %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H2a <- ifelse((estimates_sr %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_90_lower)) >
(estimates_sr %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)),
"Accepted", "Rejected")
comparison_string_sr <-
paste0("Deepfakes are ",
estimates_sr %>% filter(Parameter == "percent_comparison") %>% pull(MAP_Estimate) %>% round(1),
"% (95% CI [",
estimates_sr %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_lower) %>% round(1),
", ",
estimates_sr %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_upper) %>% round(1),
"]) as effective as genuine content in establishing self-reported evaluations")H1a
The content of the genuine videos (i.e., Source Valence) will influence participants’ self-reported evaluations. Specifically, we will use a Bayesian linear model (model 1) to estimate a 95% Confidence Interval on standardized effect size change in self-reported evaluations between Source Valence conditions in the genuine video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H1b
The content of the Deepfaked videos (i.e., Source Valence) will influence participants’ self-reported evaluations. Specifically, we will use a Bayesian linear model (model 1) to estimate a 95% Confidence Interval on standardized effect size change in self-reported evaluations between Source Valence conditions in the Deepfaked video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H2a
Change in self-reported evaluations (i.e., between Source Valence conditions) induced by Deepfaked video content will be non-inferior to genuine content.
- Result: Accepted. Deepfakes are 103.3% (95% CI [97.3, 109.4]) as effective as genuine content in establishing self-reported evaluations.
Implicit
Fit model
fit_implicit <-
brm(formula = IAT_D2 ~ source_valence * experiment_condition + (1 | experiment),
family = gaussian(),
data = data_after_exclusions,
file = "models/fit_implicit",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: IAT_D2 ~ source_valence * experiment_condition + (1 | experiment)
## Data: data_after_exclusions (Number of observations: 1346)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Group-Level Effects:
## ~experiment (Number of levels: 6)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.20 0.11 0.07 0.49 1.00 6102 9811
##
## Population-Level Effects:
## Estimate Est.Error
## Intercept 0.05 0.11
## source_valencepositive 1.32 0.07
## experiment_conditiondeepfaked 0.07 0.08
## source_valencepositive:experiment_conditiondeepfaked 0.00 0.11
## l-95% CI u-95% CI Rhat
## Intercept -0.17 0.26 1.00
## source_valencepositive 1.19 1.46 1.00
## experiment_conditiondeepfaked -0.09 0.23 1.00
## source_valencepositive:experiment_conditiondeepfaked -0.21 0.22 1.00
## Bulk_ESS Tail_ESS
## Intercept 7763 9240
## source_valencepositive 16451 18513
## experiment_conditiondeepfaked 14981 18192
## source_valencepositive:experiment_conditiondeepfaked 14243 17669
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.00 0.02 0.97 1.04 1.00 22279 19314
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_implicit) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
| b_experiment_conditiondeepfaked | uninformative |
| b_source_valencepositive.experiment_conditiondeepfaked | uninformative |
Interpret posteriors
#plot_model(fit_implicit)
plot_model(fit_implicit, type = "pred", terms = c("source_valence", "experiment_condition"))
# percent moderation
draws_imp <-
bind_cols(
select(spread_draws(fit_implicit, b_source_valencepositive), b_source_valencepositive),
select(spread_draws(fit_implicit, b_experiment_conditiondeepfaked), b_experiment_conditiondeepfaked),
select(spread_draws(fit_implicit, `b_source_valencepositive:experiment_conditiondeepfaked`), `b_source_valencepositive:experiment_conditiondeepfaked`)
) %>%
rename(main_valence = b_source_valencepositive,
main_experiment_condition = b_experiment_conditiondeepfaked,
interaction = `b_source_valencepositive:experiment_conditiondeepfaked`) %>%
mutate(effect_genuine = main_valence,
effect_deepfaked = main_valence + main_experiment_condition + interaction,
#percent_moderation = (main_experiment_condition + interaction)/main_valence *100, # alt method, same result
percent_comparison = (effect_deepfaked/effect_genuine)*100)
# results table
estimates_imp <-
map_estimate(draws_imp) %>%
full_join(bayestestR::hdi(draws_imp, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_imp, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_imp %>%
select(-percent_comparison) %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
estimates_imp %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| main_valence | 1.32 | 1.18 | 1.46 | 1.21 | 1.44 | 0.0000000 |
| main_experiment_condition | 0.06 | -0.10 | 0.23 | -0.07 | 0.20 | 0.2096429 |
| interaction | 0.00 | -0.21 | 0.22 | -0.18 | 0.18 | 0.4891071 |
| effect_genuine | 1.32 | 1.18 | 1.46 | 1.21 | 1.44 | 0.0000000 |
| effect_deepfaked | 1.39 | 1.24 | 1.55 | 1.26 | 1.52 | 0.0000000 |
| percent_comparison | 104.95 | 93.46 | 117.85 | 95.01 | 115.54 | / |
# hypothesis testing
H1c <- ifelse((estimates_imp %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H1d <- ifelse((estimates_imp %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H2b <- ifelse((estimates_imp %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_90_lower)) >
(estimates_imp %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)),
"Accepted", "Rejected")
comparison_string_imp <-
paste0("Deepfakes are ",
estimates_imp %>% filter(Parameter == "percent_comparison") %>% pull(MAP_Estimate) %>% round(1),
"% (95% CI [",
estimates_imp %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_lower) %>% round(1),
", ",
estimates_imp %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_upper) %>% round(1),
"]) as effective as genuine content in establishing self-reported evaluations")H1c
The content of the genuine videos (i.e., Source Valence) will influence participants’ IAT D2 scores. Specifically, we will use a Bayesian linear model (model 2) to estimate a 95% Confidence Interval on standardized effect size change in IAT D2 scores between Source Valence conditions in the genuine video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H1d
The content of the Deepfaked videos (i.e., Source Valence) will influence participants’ IAT D2 scores. Specifically, we will use a Bayesian linear model (model 2) to estimate a 95% Confidence Interval on standardized effect size change in IAT D2 scores between Source Valence conditions in the Deepfaked video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H2b
Change in IAT D2 scores (i.e., between Source Valence conditions) induced by Deepfaked video content will be non-inferior to genuine content.
- Result: Accepted. Deepfakes are 105% (95% CI [93.5, 117.9]) as effective as genuine content in establishing self-reported evaluations.
Behavioural intentions
Fit model
fit_intentions <-
brm(formula = mean_intentions ~ source_valence * experiment_condition, # no random effect for experiment as only exp 6 assessed intentions
family = gaussian(),
data = data_after_exclusions,
file = "models/fit_intentions",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: mean_intentions ~ source_valence * experiment_condition
## Data: data_after_exclusions (Number of observations: 204)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error
## Intercept -1.64 0.14
## source_valencepositive 1.12 0.20
## experiment_conditiondeepfaked -1.70 0.21
## source_valencepositive:experiment_conditiondeepfaked 1.95 0.28
## l-95% CI u-95% CI Rhat
## Intercept -1.92 -1.35 1.00
## source_valencepositive 0.72 1.52 1.00
## experiment_conditiondeepfaked -2.10 -1.29 1.00
## source_valencepositive:experiment_conditiondeepfaked 1.39 2.50 1.00
## Bulk_ESS Tail_ESS
## Intercept 15183 17895
## source_valencepositive 13178 15992
## experiment_conditiondeepfaked 13001 16122
## source_valencepositive:experiment_conditiondeepfaked 11385 14004
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.01 0.05 0.91 1.11 1.00 18637 17174
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_intentions) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
| b_experiment_conditiondeepfaked | uninformative |
| b_source_valencepositive.experiment_conditiondeepfaked | uninformative |
Interpret posteriors
#plot_model(fit_intentions)
plot_model(fit_intentions, type = "pred", terms = c("source_valence", "experiment_condition"))
# percent moderation
draws_intentions <-
bind_cols(
select(spread_draws(fit_intentions, b_source_valencepositive), b_source_valencepositive),
select(spread_draws(fit_intentions, b_experiment_conditiondeepfaked), b_experiment_conditiondeepfaked),
select(spread_draws(fit_intentions, `b_source_valencepositive:experiment_conditiondeepfaked`), `b_source_valencepositive:experiment_conditiondeepfaked`)
) %>%
rename(main_valence = b_source_valencepositive,
main_experiment_condition = b_experiment_conditiondeepfaked,
interaction = `b_source_valencepositive:experiment_conditiondeepfaked`) %>%
mutate(effect_genuine = main_valence,
effect_deepfaked = main_valence + main_experiment_condition + interaction,
#percent_moderation = (main_experiment_condition + interaction)/main_valence *100, # alt method, same result
percent_comparison = (effect_deepfaked/effect_genuine)*100)
# results table
estimates_intentions <-
map_estimate(draws_intentions) %>%
full_join(bayestestR::hdi(draws_intentions, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_intentions, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_intentions %>%
select(-percent_comparison) %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
estimates_intentions %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| main_valence | 1.10 | 0.73 | 1.53 | 0.78 | 1.44 | 0 |
| main_experiment_condition | -1.68 | -2.11 | -1.30 | -2.03 | -1.35 | 0 |
| interaction | 1.97 | 1.41 | 2.52 | 1.48 | 2.41 | 0 |
| effect_genuine | 1.10 | 0.73 | 1.53 | 0.78 | 1.44 | 0 |
| effect_deepfaked | 1.37 | 0.99 | 1.76 | 1.04 | 1.69 | 0 |
| percent_comparison | 118.58 | 87.52 | 169.62 | 90.93 | 158.04 | / |
# hypothesis testing
H1e <- ifelse((estimates_intentions %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H1f <- ifelse((estimates_intentions %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_95_lower)) > 0,
"Accepted", "Rejected")
H2c <- ifelse((estimates_intentions %>% filter(Parameter == "effect_deepfaked") %>% pull(CI_90_lower)) >
(estimates_intentions %>% filter(Parameter == "effect_genuine") %>% pull(CI_95_lower)),
"Accepted", "Rejected")
comparison_string_intentions <-
paste0("Deepfakes are ",
estimates_intentions %>% filter(Parameter == "percent_comparison") %>% pull(MAP_Estimate) %>% round(1),
"% (95% CI [",
estimates_intentions %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_lower) %>% round(1),
", ",
estimates_intentions %>% filter(Parameter == "percent_comparison") %>% pull(CI_95_upper) %>% round(1),
"]) as effective as genuine content in establishing self-reported evaluations")H1e
The content of the genuine videos (i.e., Source Valence) will influence participants’ behavioral intention responses. Specifically, we will use a Bayesian linear model (model 2) to estimate a 95% Confidence Interval on standardized effect size change in behavioral intention scores between Source Valence conditions in the genuine video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H1f
The content of the Deepfaked videos (i.e., Source Valence) will influence participants’ behavioral intention responses. Specifically, we will use a Bayesian linear model (model 2) to estimate a 95% Confidence Interval on standardized effect size change in behavioral intention scores between Source Valence conditions in the Deepfaked video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
H2c
Change in behavioral intentions (i.e., between Source Valence conditions) induced by Deepfaked video content will be non-inferior to genuine content.
- Result: Accepted. Deepfakes are 118.6% (95% CI [87.5, 169.6]) as effective as genuine content in establishing self-reported evaluations.
How good are people at detecting deepfakes?
Inter-rater relibility
data_after_exclusions %>%
count(deepfake_detected,
deepfake_detected_rater_1,
deepfake_detected_rater_2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| deepfake_detected | deepfake_detected_rater_1 | deepfake_detected_rater_2 | n |
|---|---|---|---|
| FALSE | FALSE | FALSE | 414 |
| FALSE | FALSE | TRUE | 16 |
| FALSE | TRUE | FALSE | 31 |
| TRUE | TRUE | TRUE | 115 |
| / | / | / | 770 |
data_after_exclusions %>%
summarize(percent_agreement = round(mean(deepfake_detected_rater_1 == deepfake_detected_rater_2, na.rm = TRUE)*100, 1)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| percent_agreement |
|---|
| 91.8 |
data_after_exclusions %>%
select(deepfake_detected_rater_1,
deepfake_detected_rater_2) %>%
as.data.frame() %>% # kappa function won't take tibbles
psych::cohen.kappa(.)## Call: cohen.kappa1(x = x, w = w, n.obs = n.obs, alpha = alpha, levels = levels)
##
## Cohen Kappa and Weighted Kappa correlation coefficients and confidence boundaries
## lower estimate upper
## unweighted kappa 0.72 0.78 0.84
## weighted kappa 0.72 0.78 0.84
##
## Number of subjects = 576Interpretation of Kappa (Altman 1999, Landis JR, 1977):
- 0.61 - 0.80 Substantial
- 0.81 - 1.00 Almost perfect
Can people accurately detect deepfakes?
- Youden’s J = sensitivity + specificity - 1, aka informedness, aka “the probability of an informed decision (as opposed to a random guess) and takes into account all predictions”
- 95% CIs were bootstrapped via case removal and the percentile method.
Sample size
data_after_exclusions %>%
count(experiment_condition,
deepfake_detected) %>%
drop_na() %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| experiment_condition | deepfake_detected | n |
|---|---|---|
| genuine | FALSE | 188 |
| genuine | TRUE | 16 |
| deepfaked | FALSE | 273 |
| deepfaked | TRUE | 99 |
Bootstrapped classification stats
if(file.exists("models/fit_classification_bootstraps.rds")){
fit_classification_bootstraps <- read_rds("models/fit_classification_bootstraps.rds")
} else {
# create bootstraps using out of bag method. makes a df with values that are collapsed dfs.
boots <- data_after_exclusions %>%
select(experiment_condition, deepfake_detected) %>%
drop_na() %>%
bootstraps(times = 2000)
# generalize to a summarize function ------
bootstrap_categorization_stats <- function(split) {
data_counts <- analysis(split) %>%
count(experiment_condition, deepfake_detected)
TP <- pull(filter(data_counts, experiment_condition == "deepfaked" & deepfake_detected == TRUE), n)
FP <- pull(filter(data_counts, experiment_condition == "genuine" & deepfake_detected == TRUE), n)
FN <- pull(filter(data_counts, experiment_condition == "deepfaked" & deepfake_detected == FALSE), n)
TN <- pull(filter(data_counts, experiment_condition == "genuine" & deepfake_detected == FALSE), n)
#accuracy <- (TP+TN)/(TP+TN+FP+FN)
sensitivity <- TP / (TP+FN)
false_negative_rate <- 1 - sensitivity
specificity <- TN / (TN+FP)
false_positive_rate <- 1 - specificity
# Youden's J statistic aka informedness aka "the probability of an informed decision (as opposed to a random guess) and takes into account all predictions". a zero value when a diagnostic test gives the same proportion of positive results for groups with and without the disease, i.e the test is useless.
informedness <- sensitivity + specificity - 1
balanced_accuracy <- (sensitivity + specificity)/2
results <-
tibble(variable = c(
#"accuracy",
"balanced_accuracy",
"informedness",
#"sensitivity",
"false_negative_rate",
#"specificity",
"false_positive_rate"
),
value = c(
#accuracy,
balanced_accuracy,
informedness,
#sensitivity,
false_negative_rate,
#specificity,
false_positive_rate
))
return(results)
}
# apply to each bootstrap
fit_classification_bootstraps <- boots %>%
mutate(categorization_stats = map(splits, bootstrap_categorization_stats)) %>%
select(-splits) %>%
unnest(categorization_stats)
write_rds(fit_classification_bootstraps, "models/fit_classification_bootstraps.rds")
}
fit_classification_bootstraps %>%
group_by(variable) %>%
summarize(median = quantile(value, 0.500),
ci_lower = quantile(value, 0.025),
ci_upper = quantile(value, 0.975),
.groups = "drop") %>%
mutate_if(is.numeric, round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| variable | median | ci_lower | ci_upper |
|---|---|---|---|
| balanced_accuracy | 0.59 | 0.56 | 0.62 |
| false_negative_rate | 0.73 | 0.69 | 0.78 |
| false_positive_rate | 0.08 | 0.04 | 0.12 |
| informedness | 0.19 | 0.13 | 0.25 |
H3: Participants are poor at making accurate and informed judgements about whether online video content is genuine or Deepfaked. Our predictions here are descriptive/continuous rather than involving cut-off based inference rules.
H3a
We expect participants to be poor at correctly detecting Deepfakes (i.e., demonstrate a high false negative rate, FNR ≳ .80).
H3b
We expect participants to incorrectly detect Deepfakes even when the video content was real (i.e., demonstrate a high false positive rate, FPR ≳ .05).
H3c
We expect participants to be poor at making accurate decisions about whether content is genuine or not (i.e., balanced accuracy not greatly above chance, ≲ .60).
H3d
We expect participants to make poorly informed decisions about whether content is genuine or not (i.e., informedness/Youden’s J ≲ .25).
Even the subset of participants who were aware of the concept of deepfakes before the study?
Sample size
data_after_exclusions %>%
filter(deepfake_concept_check == TRUE) %>%
count(experiment_condition,
deepfake_detected) %>%
drop_na() %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| experiment_condition | deepfake_detected | n |
|---|---|---|
| genuine | FALSE | 96 |
| genuine | TRUE | 10 |
| deepfaked | FALSE | 82 |
| deepfaked | TRUE | 32 |
Bootstrapped classification stats
if(file.exists("models/fit_classification_bootstraps_subset.rds")){
fit_classification_bootstraps_subset <- read_rds("models/fit_classification_bootstraps_subset.rds")
} else {
# create bootstraps using out of bag method. makes a df with values that are collapsed dfs.
boots <- data_after_exclusions %>%
filter(deepfake_concept_check == TRUE) %>%
select(experiment_condition, deepfake_detected) %>%
drop_na() %>%
bootstraps(times = 2000)
# generalize to a summarize function ------
bootstrap_categorization_stats <- function(split) {
data_counts <- analysis(split) %>%
count(experiment_condition, deepfake_detected)
TP <- pull(filter(data_counts, experiment_condition == "deepfaked" & deepfake_detected == TRUE), n)
FP <- pull(filter(data_counts, experiment_condition == "genuine" & deepfake_detected == TRUE), n)
FN <- pull(filter(data_counts, experiment_condition == "deepfaked" & deepfake_detected == FALSE), n)
TN <- pull(filter(data_counts, experiment_condition == "genuine" & deepfake_detected == FALSE), n)
#accuracy <- (TP+TN)/(TP+TN+FP+FN)
sensitivity <- TP / (TP+FN)
false_negative_rate <- 1 - sensitivity
specificity <- TN / (TN+FP)
false_positive_rate <- 1 - specificity
# Youden's J statistic aka informedness aka "the probability of an informed decision (as opposed to a random guess) and takes into account all predictions". a zero value when a diagnostic test gives the same proportion of positive results for groups with and without the disease, i.e the test is useless.
informedness <- sensitivity + specificity - 1
balanced_accuracy <- (sensitivity + specificity)/2
results <-
tibble(variable = c(
#"accuracy",
"balanced_accuracy",
"informedness",
#"sensitivity",
"false_negative_rate",
#"specificity",
"false_positive_rate"
),
value = c(
#accuracy,
balanced_accuracy,
informedness,
#sensitivity,
false_negative_rate,
#specificity,
false_positive_rate
))
return(results)
}
# apply to each bootstrap
fit_classification_bootstraps_subset <- boots %>%
mutate(categorization_stats = map(splits, bootstrap_categorization_stats)) %>%
select(-splits) %>%
unnest(categorization_stats)
write_rds(fit_classification_bootstraps_subset, "models/fit_classification_bootstraps_subset.rds")
}
fit_classification_bootstraps_subset %>%
group_by(variable) %>%
summarize(median = quantile(value, 0.500),
ci_lower = quantile(value, 0.025),
ci_upper = quantile(value, 0.975),
.groups = "drop") %>%
mutate_if(is.numeric, round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| variable | median | ci_lower | ci_upper |
|---|---|---|---|
| balanced_accuracy | 0.59 | 0.54 | 0.64 |
| false_negative_rate | 0.72 | 0.63 | 0.80 |
| false_positive_rate | 0.09 | 0.04 | 0.15 |
| informedness | 0.19 | 0.09 | 0.28 |
Does prior knowledge of deepfakes make people better at detecting them?
Putting aside true negatives and false positive, does prior awareness of the concept of deepfaking at least make people better at detecting deepfakes
It would of course be possible include data from both experiment_conditions and add it to the model, however interpreting the two and three way interactions is less intuitive. Given this question is of secondary importance, I we therefore elected for the simpler analysis focusing on awareness and the FNR/TPR.
# convert data to counts
data_counts <- data_after_exclusions %>%
filter(experiment_condition == "deepfaked") %>%
dplyr::select(deepfake_concept_check, deepfake_detected) %>%
drop_na() %>%
count(deepfake_concept_check, deepfake_detected) %>%
mutate(counts = n,
awareness = as.factor(deepfake_concept_check),
detection = as.factor(deepfake_detected),
proportion = counts/sum(counts)) %>%
dplyr::select(awareness, detection, counts, proportion)
# total counts is needed later to convert to proportions
total_counts <- data_counts %>%
summarize(total = sum(counts)) %>%
pull(total)
# fit poisson model
fit_poisson_detection_awareness <-
brm(formula = counts ~ 1 + awareness * detection,
family = poisson(),
data = data_counts,
file = "models/fit_poisson_detection_awareness",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99,
max_treedepth = 15), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -mmacosx-version-min=10.13 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1Inspect convergence
## Family: poisson
## Links: mu = log
## Formula: counts ~ 1 + awareness * detection
## Data: data_counts (Number of observations: 4)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 4.39 0.11 4.16 4.60 1.00 16652
## awarenessTRUE 0.01 0.16 -0.30 0.32 1.00 13088
## detectionTRUE -1.94 0.32 -2.60 -1.36 1.00 9083
## awarenessTRUE:detectionTRUE 0.99 0.38 0.28 1.76 1.00 9390
## Tail_ESS
## Intercept 17197
## awarenessTRUE 15102
## detectionTRUE 10543
## awarenessTRUE:detectionTRUE 11766
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_poisson_detection_awareness) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_awarenessTRUE | uninformative |
| b_detectionTRUE | uninformative |
| b_awarenessTRUE.detectionTRUE | uninformative |
Interpret posteriors
Plots
Table
Parameter estimates
# posterior draws for parameters (for results table)
draws_detection_awareness <- posterior_samples(fit_poisson_detection_awareness) %>%
dplyr::select(awarenessTRUE = b_awarenessTRUE,
detectionTRUE = b_detectionTRUE,
interaction = `b_awarenessTRUE:detectionTRUE`)
full_join(as_tibble(map_estimate(draws_detection_awareness)),
as.tibble(bayestestR::hdi(draws_detection_awareness, ci = .95)),
by = "Parameter") %>%
mutate_if(is.numeric, exp) %>%
dplyr::select(Parameter, incidence_rate_ratio_MAP = MAP_Estimate, CI_95_lower = CI_low, CI_95_upper = CI_high) %>%
# convert from odds to probability
# mutate_if(is.numeric, function(x){x/(1+x)}) %>%
mutate_if(is.numeric, round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | incidence_rate_ratio_MAP | CI_95_lower | CI_95_upper |
|---|---|---|---|
| awarenessTRUE | 1.03 | 0.75 | 1.38 |
| detectionTRUE | 0.15 | 0.08 | 0.27 |
| interaction | 2.60 | 1.27 | 5.56 |
- Evidence non-zero interaction effect: incident rate ratio was > 1.
- Results therefore suggest that aware participants were 2.6 times more likely to detect a deepfake than those who were not.
- Predicted percentage changes of detecting are below:
Predicted probabilities
posterior_predictions_detection_awareness <-
tibble(awareness = c("TRUE", "FALSE"),
detection = c("TRUE", "FALSE")) %>%
data_grid(awareness, detection) %>%
add_predicted_draws(model = fit_poisson_detection_awareness) %>%
rename(predicted_count = .prediction) %>%
mutate(predicted_probabiity = predicted_count/total_counts) %>%
ungroup() %>%
dplyr::select(awareness, detection, predicted_probabiity)
posterior_predictions_detection_awareness_aT_dT <- posterior_predictions_detection_awareness %>%
filter(awareness == "TRUE" & detection == "TRUE")
posterior_predictions_detection_awareness_aT_dF <- posterior_predictions_detection_awareness %>%
filter(awareness == "TRUE" & detection == "FALSE")
posterior_predictions_detection_awareness_aF_dT <- posterior_predictions_detection_awareness %>%
filter(awareness == "FALSE" & detection == "TRUE")
posterior_predictions_detection_awareness_aF_dF <- posterior_predictions_detection_awareness %>%
filter(awareness == "FALSE" & detection == "FALSE")
results_detection_probabilities <-
rbind(
bind_cols(as_tibble(map_estimate(posterior_predictions_detection_awareness_aT_dT$predicted_probabiity)),
as.tibble(bayestestR::hdi(posterior_predictions_detection_awareness_aT_dT$predicted_probabiity,
ci = .95))) %>%
mutate(awareness = "TRUE", detection = "TRUE"),
bind_cols(as_tibble(map_estimate(posterior_predictions_detection_awareness_aT_dF$predicted_probabiity)),
as.tibble(bayestestR::hdi(posterior_predictions_detection_awareness_aT_dF$predicted_probabiity,
ci = .95))) %>%
mutate(awareness = "TRUE", detection = "FALSE"),
bind_cols(as_tibble(map_estimate(posterior_predictions_detection_awareness_aF_dT$predicted_probabiity)),
as.tibble(bayestestR::hdi(posterior_predictions_detection_awareness_aF_dT$predicted_probabiity,
ci = .95))) %>%
mutate(awareness = "FALSE", detection = "TRUE"),
bind_cols(as_tibble(map_estimate(posterior_predictions_detection_awareness_aF_dF$predicted_probabiity)),
as.tibble(bayestestR::hdi(posterior_predictions_detection_awareness_aF_dF$predicted_probabiity,
ci = .95))) %>%
mutate(awareness = "FALSE", detection = "FALSE")
) %>%
dplyr::select(awareness, detection, detection_probability_MAP = value,
CI_95_lower = CI_low, CI_95_upper = CI_high) %>%
mutate_if(is.numeric, round, digits = 3)
results_detection_probabilities %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| awareness | detection | detection_probability_MAP | CI_95_lower | CI_95_upper |
|---|---|---|---|---|
| TRUE | TRUE | 0.145 | 0.087 | 0.237 |
| TRUE | FALSE | 0.379 | 0.280 | 0.522 |
| FALSE | TRUE | 0.043 | 0.019 | 0.106 |
| FALSE | FALSE | 0.380 | 0.275 | 0.512 |
- Probability of detecting deepfake if unaware: 0.043
- Probability of detecting deepfake if aware: 0.145
Does detecting a deepfake make you immune to it?
Subset who received deepfaked videos but also detected them. Same Bayesian multilevel models as employed above, using only source_valence as IV, i.e., to detect whether learning effects are credibly non-zero in this subset.
Sample sizes
data_detectors_subset <- data_after_exclusions %>%
filter(experiment_condition == "deepfaked" & deepfake_detected == TRUE)
data_detectors_subset %>%
count(source_valence) %>%
rename(n_experiments_4_to_6 = n) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| source_valence | n_experiments_4_to_6 |
|---|---|
| negative | 51 |
| positive | 48 |
data_detectors_subset %>%
filter(experiment == 6) %>%
count(source_valence) %>%
rename(n_experiment_6 = n) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| source_valence | n_experiment_6 |
|---|---|
| negative | 14 |
| positive | 10 |
Intentions DV present only in exp 6. N is particularly low for this analysis, so results should be taken with additional caution.
Self-reported evaluations
Fit model
fit_selfreport_deepfaked_detected <-
brm(formula = mean_self_reported_evaluation ~ source_valence + (1 | experiment),
family = gaussian(),
data = data_detectors_subset,
file = "models/fit_selfreport_deepfaked_detected",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: mean_self_reported_evaluation ~ source_valence + (1 | experiment)
## Data: data_detectors_subset (Number of observations: 99)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Group-Level Effects:
## ~experiment (Number of levels: 3)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.44 0.55 0.01 1.96 1.00 5085 4924
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -1.60 0.37 -2.40 -0.85 1.00 6252
## source_valencepositive 2.75 0.24 2.28 3.22 1.00 17481
## Tail_ESS
## Intercept 5208
## source_valencepositive 15763
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.17 0.09 1.02 1.36 1.00 16377 16890
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_selfreport_deepfaked_detected) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
Interpret posteriors
#plot_model(fit_selfreport_deepfaked_detected)
plot_model(fit_selfreport_deepfaked_detected, type = "pred", terms = "source_valence")
# results table
draws_sr_deepfaked_detected <-
select(spread_draws(fit_selfreport_deepfaked_detected, b_source_valencepositive), b_source_valencepositive) %>%
rename(effect_deepfaked_detected = b_source_valencepositive)
estimates_sr_deepfaked_detected <-
map_estimate(draws_sr_deepfaked_detected) %>%
full_join(bayestestR::hdi(draws_sr_deepfaked_detected, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_sr_deepfaked_detected, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_sr_deepfaked_detected %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
bind_rows(filter(estimates_sr, Parameter %in% c("effect_deepfaked")),
estimates_sr_deepfaked_detected) %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| effect_deepfaked | 2.78 | 2.63 | 2.95 | 2.66 | 2.93 | 0 |
| effect_deepfaked_detected | 2.74 | 2.27 | 3.21 | 2.36 | 3.14 | 0 |
# hypothesis testing
H4a <- ifelse((estimates_sr_deepfaked_detected %>% filter(Parameter == "effect_deepfaked_detected") %>%
pull(CI_95_lower)) > 0,
"Accepted", "Rejected")H4a
In the subset of participants who were shown a Deepfaked video and accurately detected that the video was Deepfaked, the content of the Deepfaked videos (i.e., Source Valence) will influence participants’ self-reported evaluations. Specifically, we will use a Bayesian linear model (model 3) to estimate a 95% Confidence Interval on standardized effect size change in self-reported evaluations between Source Valence conditions in the genuine video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
Implicit
Fit model
fit_implicit_deepfaked_detected <-
brm(formula = IAT_D2 ~ source_valence + (1 | experiment),
family = gaussian(),
data = data_detectors_subset,
file = "models/fit_implicit_deepfaked_detected",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: IAT_D2 ~ source_valence + (1 | experiment)
## Data: data_detectors_subset (Number of observations: 99)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Group-Level Effects:
## ~experiment (Number of levels: 3)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.04 0.81 0.24 3.26 1.00 5697 9416
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.07 0.67 -1.35 1.52 1.00 6969
## source_valencepositive 1.07 0.19 0.70 1.43 1.00 18710
## Tail_ESS
## Intercept 7143
## source_valencepositive 16473
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.91 0.07 0.79 1.06 1.00 17772 15970
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_implicit_deepfaked_detected) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
Interpret posteriors
#plot_model(fit_implicit_deepfaked_detected)
plot_model(fit_implicit_deepfaked_detected, type = "pred", terms = "source_valence")
# results table
draws_imp_deepfaked_detected <-
select(spread_draws(fit_implicit_deepfaked_detected, b_source_valencepositive), b_source_valencepositive) %>%
rename(effect_deepfaked_detected = b_source_valencepositive)
estimates_imp_deepfaked_detected <-
map_estimate(draws_imp_deepfaked_detected) %>%
full_join(bayestestR::hdi(draws_imp_deepfaked_detected, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_imp_deepfaked_detected, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_imp_deepfaked_detected %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
bind_rows(filter(estimates_imp, Parameter %in% c("effect_deepfaked")),
estimates_imp_deepfaked_detected) %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| effect_deepfaked | 1.39 | 1.24 | 1.55 | 1.26 | 1.52 | 0 |
| effect_deepfaked_detected | 1.05 | 0.69 | 1.42 | 0.76 | 1.37 | 0 |
# hypothesis testing
H4b <- ifelse((estimates_imp_deepfaked_detected %>% filter(Parameter == "effect_deepfaked_detected") %>%
pull(CI_95_lower)) > 0,
"Accepted", "Rejected")H4b
In the subset of participants who were shown a Deepfaked video and accurately detected that the video was Deepfaked, the content of the Deepfaked videos (i.e., Source Valence) will influence participants’ IAT D2 scores. Specifically, we will use a Bayesian linear model (model 4) to estimate a 95% Confidence Interval on standardized effect size change in IAT D2 scores between Source Valence conditions in the Deepfaked video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
Behavioural intentions
Fit model
fit_intentions_deepfaked_detected <-
brm(formula = mean_intentions ~ source_valence, # no random effect for experiment as only exp 6 assessed intentions
family = gaussian(),
data = data_detectors_subset,
file = "models/fit_intentions_deepfaked_detected",
prior = prior(normal(0, 10)),
iter = 10000,
warmup = 3000,
control = list(adapt_delta = 0.99), # to avoid divergent transitions
chains = 4,
cores = parallel::detectCores())Inspect convergence
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: mean_intentions ~ source_valence
## Data: data_detectors_subset (Number of observations: 24)
## Samples: 4 chains, each with iter = 10000; warmup = 3000; thin = 1;
## total post-warmup samples = 28000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -3.27 0.27 -3.80 -2.75 1.00 18627
## source_valencepositive 2.71 0.42 1.88 3.53 1.00 18437
## Tail_ESS
## Intercept 15502
## source_valencepositive 15269
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.99 0.16 0.74 1.36 1.00 16714 15060
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Check informativeness of prior
Using Gelman’s (2019) simple heuristic: For each parameter, compare the posterior sd to the prior sd. If the posterior sd for any parameter is more than 0.1 times the prior sd, then note that the prior was informative.
check_prior(fit_intentions_deepfaked_detected) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | Prior_Quality |
|---|---|
| b_Intercept | uninformative |
| b_source_valencepositive | uninformative |
Interpret posteriors
#plot_model(fit_intentions_deepfaked_detected)
plot_model(fit_intentions_deepfaked_detected, type = "pred", terms = "source_valence")
# results table
draws_intentions_deepfaked_detected <-
select(spread_draws(fit_intentions_deepfaked_detected, b_source_valencepositive), b_source_valencepositive) %>%
rename(effect_deepfaked_detected = b_source_valencepositive)
estimates_intentions_deepfaked_detected <-
map_estimate(draws_intentions_deepfaked_detected) %>%
full_join(bayestestR::hdi(draws_intentions_deepfaked_detected, ci = .95) %>%
rename(CI_95_lower = CI_low,
CI_95_upper = CI_high) %>%
as_tibble(),
by = "Parameter") %>%
full_join(bayestestR::hdi(draws_intentions_deepfaked_detected, ci = .90) %>%
as_tibble() %>%
rename(CI_90_lower = CI_low,
CI_90_upper = CI_high),
by = "Parameter") %>%
full_join(draws_intentions_deepfaked_detected %>%
gather(Parameter, value) %>%
group_by(Parameter) %>%
summarize(pd = mean(value > 0)) %>%
mutate(p = pd_to_p(pd, direction = "one-sided")) %>%
ungroup() %>%
select(Parameter, p),
by = "Parameter") %>%
select(Parameter, MAP_Estimate, CI_95_lower, CI_95_upper,
CI_90_lower, CI_90_upper, p)
bind_rows(filter(estimates_intentions, Parameter %in% c("effect_deepfaked")),
estimates_intentions_deepfaked_detected) %>%
mutate_at(.vars = c("MAP_Estimate", "CI_95_lower", "CI_95_upper", "CI_90_lower", "CI_90_upper"), round, digits = 2) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = FALSE)| Parameter | MAP_Estimate | CI_95_lower | CI_95_upper | CI_90_lower | CI_90_upper | p |
|---|---|---|---|---|---|---|
| effect_deepfaked | 1.37 | 0.99 | 1.76 | 1.04 | 1.69 | 0 |
| effect_deepfaked_detected | 2.72 | 1.87 | 3.51 | 2.03 | 3.39 | 0 |
# hypothesis testing
H4c <- ifelse((estimates_intentions_deepfaked_detected %>% filter(Parameter == "effect_deepfaked_detected") %>%
pull(CI_95_lower)) > 0,
"Accepted", "Rejected")H4c
In the subset of participants who were shown a Deepfaked video and accurately detected that the video was Deepfaked, the content of the Deepfaked videos (i.e., Source Valence) will influence participants’ behavioral intention scores. Specifically, we will use a Bayesian linear model (model 4) to estimate a 95% Confidence Interval on standardized effect size change in behavioral intention scores between Source Valence conditions in the Deepfaked video condition subgroup. Confidence Intervals whose lower bounds are > 0 will be considered evidence in support of this hypothesis.
- Result: Accepted
Session Info
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_IE.UTF-8/en_IE.UTF-8/en_IE.UTF-8/C/en_IE.UTF-8/en_IE.UTF-8
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] modelr_0.1.8 semTools_0.5-3 lavaan_0.6-7 IATscores_0.2.7
## [5] broom_0.7.2 rsample_0.0.7 psych_2.0.9 sjPlot_2.8.4
## [9] bayestestR_0.7.5 tidybayes_2.0.3 brms_2.14.0 Rcpp_1.0.5
## [13] kableExtra_1.3.1 knitr_1.30 forcats_0.5.0 stringr_1.4.0
## [17] dplyr_1.0.2 purrr_0.3.4 readr_1.3.1 tidyr_1.1.2
## [21] tibble_3.0.4 ggplot2_3.3.2 tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
## [1] tidyselect_1.1.0 lme4_1.1-25 htmlwidgets_1.5.1
## [4] grid_4.0.2 munsell_0.5.0 codetools_0.2-16
## [7] effectsize_0.4.0 statmod_1.4.34 DT_0.13
## [10] future_1.19.1 miniUI_0.1.1.1 withr_2.3.0
## [13] Brobdingnag_1.2-6 colorspace_2.0-0 highr_0.8
## [16] rstudioapi_0.13 stats4_4.0.2 bayesplot_1.7.2
## [19] listenv_0.8.0 labeling_0.4.2 huge_1.3.4.1
## [22] emmeans_1.4.6 rstan_2.21.2 mnormt_1.5-7
## [25] farver_2.0.3 bridgesampling_1.0-0 coda_0.19-3
## [28] vctrs_0.3.5 generics_0.0.2 TH.data_1.0-10
## [31] xfun_0.19 R6_2.5.0 markdown_1.1
## [34] assertthat_0.2.1 promises_1.1.0 scales_1.1.1
## [37] multcomp_1.4-13 nnet_7.3-14 gtable_0.3.0
## [40] globals_0.13.1 processx_3.4.4 sandwich_2.5-1
## [43] rlang_0.4.8 splines_4.0.2 checkmate_2.0.0
## [46] inline_0.3.16 yaml_2.2.1 reshape2_1.4.4
## [49] abind_1.4-5 d3Network_0.5.2.1 threejs_0.3.3
## [52] crosstalk_1.1.0.1 backports_1.1.9 httpuv_1.5.2
## [55] rsconnect_0.8.16 Hmisc_4.4-1 tools_4.0.2
## [58] ellipsis_0.3.1 RColorBrewer_1.1-2 ggridges_0.5.2
## [61] plyr_1.8.6 base64enc_0.1-3 ps_1.4.0
## [64] prettyunits_1.1.1 rpart_4.1-15 pbapply_1.4-2
## [67] zoo_1.8-8 qgraph_1.6.5 haven_2.3.1
## [70] cluster_2.1.0 fs_1.4.1 furrr_0.2.1
## [73] magrittr_2.0.1 data.table_1.13.2 colourpicker_1.0
## [76] reprex_0.3.0 mvtnorm_1.1-1 whisker_0.4
## [79] sjmisc_2.8.5 matrixStats_0.56.0 hms_0.5.3
## [82] shinyjs_1.1 mime_0.9 evaluate_0.14
## [85] arrayhelpers_1.1-0 xtable_1.8-4 shinystan_2.5.0
## [88] sjstats_0.18.0 jpeg_0.1-8.1 readxl_1.3.1
## [91] gridExtra_2.3 ggeffects_0.14.3 rstantools_2.1.1
## [94] compiler_4.0.2 V8_3.2.0 crayon_1.3.4
## [97] minqa_1.2.4 StanHeaders_2.21.0-6 htmltools_0.5.0
## [100] corpcor_1.6.9 later_1.0.0 Formula_1.2-3
## [103] RcppParallel_5.0.2 lubridate_1.7.9 DBI_1.1.0
## [106] sjlabelled_1.1.7 dbplyr_1.4.3 MASS_7.3-53
## [109] boot_1.3-25 Matrix_1.2-18 cli_2.1.0
## [112] insight_0.10.0 igraph_1.2.5 BDgraph_2.62
## [115] pkgconfig_2.0.3 foreign_0.8-80 xml2_1.3.2
## [118] svUnit_1.0.3 pbivnorm_0.6.0 dygraphs_1.1.1.6
## [121] webshot_0.5.2 estimability_1.3 rvest_0.3.5
## [124] snakecase_0.11.0 callr_3.5.1 digest_0.6.27
## [127] parameters_0.8.6 rmarkdown_2.5 cellranger_1.1.0
## [130] htmlTable_1.13.3 curl_4.3 shiny_1.5.0
## [133] gtools_3.8.2 rjson_0.2.20 nloptr_1.2.2.2
## [136] glasso_1.11 lifecycle_0.2.0 nlme_3.1-148
## [139] jsonlite_1.7.1 viridisLite_0.3.0 fansi_0.4.1
## [142] pillar_1.4.6 lattice_0.20-41 loo_2.3.1
## [145] fastmap_1.0.1 httr_1.4.1 pkgbuild_1.1.0
## [148] survival_3.1-12 glue_1.4.2 xts_0.12-0
## [151] fdrtool_1.2.15 png_0.1-7 shinythemes_1.1.2
## [154] stringi_1.4.6 performance_0.4.6 latticeExtra_0.6-29